1. What is F Test

F-Test stands for Fisher's test. Generally, this is the test used to Compare to variances.

2. Procedure of F-Test

The step by step procedure is given below. Although in solving a typical problem, we may have more steps if we further break down a step into two.

Step 1: Set up the null and alternate hypothesis

Step 2: Calculate the variaces of the two groups

Step 3: Calculate the F-Statistic

Step 4: Look up the F value from Statistical Tables

Step 5: Draw you conclusion

3. An Example (Question 12)

In a packaging plant, a machine packs cartons with jars. It is supposed
that a new machine would pack faster on the average than the machine
currently used. To test the hypothesis, the time it takes each machine
to pack ten carons are recorded. The result in seconds is as follows.

New Machine: 42,41,41.3,41.8,42.4,42.8,43.2,42.3,41.8,42.7
Old Machine: 42.7,43.6,43.8,43.3,42.5,43.5,43.1,41.7,44,44.1

Perform an F-test to determine if the null hypothesis should be accepted.

4. Solution Steps

As usual, we need to understand the question to be able to set up the null and the alternate hypothesis.
The null hypotheisis is what is currently believed and we want to test if we would continue to accept it or not.
From the question, the current believe is that the new machine is better. Which means that the means of the two machines are different.
The alternate hypothesis is the opposite of the null hypothesis. So let's state them

Step 1: State the null and althernate hypothesisH0: μ1 ≠ μ2Ha: μ1 = μ2Note:
The null hypothesis says that the new machine is better. If this is the
case, then the mean of the two samples would not be equal. That is the
null hypothesis

If you have transfered this data to excel, you can easily find the
means using the AVERAGE() function in excel. You will have a table like
the on shown in Figure 1.

Table 1

Step 3: Calculate Deviations from the means for the two groups
The deviations are gotten by subtracting the mean from each of the values. Do this for the two groups. After doing this the excel file would be as shown in Figure 2 with the D column calculated.

Table 2

Step 4: Calculate the Squared Deviations
This step is very easy. Just take the square of the deviationss

Step 5: Take sum of the Squared Deviations
In this step, you take the sum of the Squared Deviation (D^2) column. If you have done this correctly, your excel sheet would look like the following.

Table 3

Step 6: Calculate the Variances of the two Groups
We would calculate this by hand using the values from the excel sheet. Then we also calculate this value automatically using excel formulas. The caluclation by hand is given below:

Remember: The variance is the square of the standard deviation. The is why we have s in the formula(for Standard deviation)

Step 7: Calculate the F-Statistic
The F statistic is simply gotten by dividing the Variance 1 by the Variance 2. This given by the forumula:

F = Var2/Var1

You can calculate this by hand and also using the excel sheet we have been working on. At this point, the excel sheet would look like shown in the Table 4